PARTICULARLY APPLICABLE TO SOME GEODETICAL PROBLEMS. 117 



^ = £l 

 x' c 



- = - 



s _ ff 



y' ~ «' 



XX' = yij = zz'j 



X 



y' 



X 



y 



14. In the triangle ABC, the angle a is the sum of the three 

 angles A, ABB, ACD, of which the last two are equal to the angles 

 BAD', C'A'D' that make up A', hence we have this property : 



A + A' = a, B + B' = fi, C+ C = 



II. 



The affinity of the two triangles in respect of these, and other pro- 

 perties which are to follow, may not improperly be indicated by calling 

 them Conjugate Triangles. 



15. Because A = a - A', and A' = a - A, also, similarly, 



B = 0- B, B = fi-B, C=y- C, C = y - C, 



the formulae of Art. 11. gives us these, 



be . 

 = — sm A 



X 



a; sin a -|- y sin /3 + » sin 7 = — sin B' ^ 



ab . 

 = — sm C 



b'c' . 

 = — r sm A 



X 



a'c' 

 x' sin a + y' sin i3 + ss' sin v > = — 7- sin B 



] y J 



all . 

 = — - sm C 



III. 



